I was reading Calculus Volume 1 page 211, and was confused about the situation applying the epsilon-delta definition when the limit does not exist.
According the the book, "The lim does not exist if for every real number $L$, there exists a real number $\epsilon > 0$ so that for all $\delta > 0$, there is an $x$ satisfying $0 < |x - a| < \epsilon$, so that $|f(x) - L| \geq \delta$."
As delta and epsilon represent the margins from the a and L, thus both will be bigger than 0, following the definition, we can make up (what is proving something? for me this is making up some special case to "prove" something) some delta and epsilon combination satisfying the condition to "prove" it.
But where does this definition come from? I really want to know this, please help me
